The invention resides in an x-ray lens for the focusing of x-rays.
x-ray lenses for focusing x-rays consist generally of a large number N of individual focusing elements which are called lens elements.
A. Snigirev, B. Kohn, I. Snigireva, A. Souvorov and B. lengeler, Focusing High-Energy X-rays by compound refractive lenses, Applied Optics, vol. 37, 1998, pages 653-662, discloses lens elements which have a parabolic profile that can be defined by the equationY(x)−x2/2r.  (1)
Herein, x designates the parabola axis and ½r is the semi-parameter of the parabola (see for example, Bronstein, Semendjajew, Taschenbuch der Mathematik, 20th edition, 1981, page 278).
Considering the real part δ of the refraction number n=1+iβ−δ, for this type of x-ray lenses with a wavelength λ, the focal spot size σ is obtained as:σ=0.68√{square root over (λδ(E)F)},  (2)wherein F is the focal length of the lens element and E is the photon energy and δ(E)˜E−2. With wavelengths in the range of the x-ray radiation, that is, about between 0.01 and 1 nm, ideally focal spots of a size σ of less than 0.1 μm can be obtained herewith.
The focal depth FWHM is a measure for the energy range, in which the lens can be considered to be focusing and is defined for lenses with a parabolic profile Y(x) in accordance with the equation (1) by
                    FWHM        =                                            (                                                πβ                                      4                    ⁢                    δ                                                  ⁢                F                            )                        2                                              (        3        )            
For known x-ray lenses, this is only a few millimeters which corresponds to an energy range of 0.1% of the nominal energy, that is, a few electron volts (ev).
X-ray spectroscope examinations however require over a wide energy range of the photons, preferably over several keV at a fixed location where particularly the sample to be analyzed is located, a constant size of the focal spot which should be less than 1 μm. For example, with EXAFS examinations the energy ranged ΔE to be covered is about 1 keV; with XANES examinations, it is about 100 eV.
The focal length of a lens with a large focal depth can be defined by the equation: F(E)=( r+f(x))/2Nδ(E)  (4)wherein F(E) is the focal length measured from the center of the lens to the center of the focal spot, ( r+f(x)) is the lens curvature radius averaged over the lens aperture and N is the number of the focusing elements of the lens. According to equation 4, the sample is disposed over a focal depth ΔF within the focal spot, when the energy varies by the amount
                              Δ          ⁢                                          ⁢          E                =                                            Δ              ⁢                                                          ⁢              F                        F                    ·                      E            2                                              (        5        )            If for E an average value of 12.7 keV and a typical focal length of 18 cm is selected then a focal depth of ΔF=2.8 cm is obtained for the energy range ΔE of about 1 keV to be covered by the EXAFS examinations.
On the basis of these facts, it is the object of the present invention to provide x-ray lenses which focus the incident x-ray radiation over a large energy range at a fixed location. In particular, an x-ray lens is to be provided which, with a fixed energy, has, over a focal depth of several centimeters, a focal spot with a half value width of less than 1 μm, wherein the limits of the focal depth area determined by those areas where the half value width of the focal spot is greater than 1 μm.